Stable optimizationless recovery from phaseless linear measurements
Numerical Analysis
2013-10-08 v4
Abstract
We address the problem of recovering an n-vector from m linear measurements lacking sign or phase information. We show that lifting and semidefinite relaxation suffice by themselves for stable recovery in the setting of m = O(n log n) random sensing vectors, with high probability. The recovery method is optimizationless in the sense that trace minimization in the PhaseLift procedure is unnecessary. That is, PhaseLift reduces to a feasibility problem. The optimizationless perspective allows for a Douglas-Rachford numerical algorithm that is unavailable for PhaseLift. This method exhibits linear convergence with a favorable convergence rate and without any parameter tuning.
Cite
@article{arxiv.1208.1803,
title = {Stable optimizationless recovery from phaseless linear measurements},
author = {Laurent Demanet and Paul Hand},
journal= {arXiv preprint arXiv:1208.1803},
year = {2013}
}